Models That Change With Experience

Persistent AI requires more than long context.

A system interacting with the same person, biological system, robot, environment, or artificial agent over months or years encounters a continuously changing process.

Its internal state is only partially observable. Different components evolve at different timescales. Observations are incomplete and sometimes contradictory. The meaning of an earlier observation may only become clear after later evidence arrives. Most importantly, the dynamics of the individual system are not necessarily known in advance.

Let the subject have latent state $z_t$, produce observations $o_t$, and receive actions $a_t$. A persistent state estimator attempts to infer

This is necessary but insufficient. The transition dynamics themselves may be uncertain:

where ${\theta }_t$ describes the system's currently inferred dynamics.

The problem is therefore not simply: what state is the system in? It is simultaneously:

What state is it in, what dynamics produced that state, how will those dynamics respond to intervention, and which parts of our current explanation are wrong?

This changes the role of memory. Memory becomes the substrate from which an evolving model of dynamics can be constructed.

At time $t$, represent the system's internal model as

• $Z_t$ is the longitudinal estimate of latent state;
• ${\Theta }_t$ represents learned transition dynamics;
• $H_t$ is a set of competing hypotheses about those dynamics;
• $G_t$ is a temporal dependency structure connecting evidence, states, hypotheses, predictions, and actions;
• ${\Pi }_t$ represents the current action policy.

The model spans three temporal regions:

The past contains observations and reconstructed states. The present contains the current state distribution and active hypotheses. The future contains predicted states, expected observations, candidate actions, and target states.

These are not independent stores. They are parts of the same dependency structure. A future prediction depends on a hypothesis. The hypothesis depends on inferred states. Those states depend on observations. If an observation changes the interpretation of an earlier state, consequences can propagate through the model.

The update is therefore not simply

Instead:

where $\mathcal{R}$ is a reconciliation operator capable of modifying dependent parts of the model.

A persistent system faces a fundamental asymmetry. What happened cannot change. What the system believes happened can.

Suppose observations available at time $t$ produce an inferred historical state

A later observation $o_{t+k}$ provides evidence that changes the interpretation of that earlier period. The system produces

The underlying observation is not rewritten. A new version of the derived state is created with explicit provenance linking it to both the original evidence and the evidence that caused reinterpretation.

This distinction allows the model to preserve two things simultaneously:

• epistemic plasticity — the ability to change its interpretation;
• epistemic traceability — the ability to reconstruct why it previously believed something else.

The model has a revisable past without having an editable history.

Naively reconsidering the complete history after every observation is computationally undesirable. Continuous plasticity therefore requires explicit dependency structure.

A state estimate records which observations and intermediate inferences produced it. Hypotheses record the states and evidence on which they depend. Predictions depend on hypotheses. Planned actions depend on predicted states. When new evidence arrives, the model identifies the affected dependency subgraph.

But only reachable dependent nodes need to be reconsidered. If the complete graph contains $N$ nodes but an observation affects a dependency subgraph containing $k$ nodes, reconciliation can scale approximately with $O(k)$ rather than requiring global reconstruction over $O(N)$.

Plasticity can therefore remain local even when memory becomes large — the cost of having a long history should not require reasoning over the entire history on every interaction.

A world model should distinguish what it observes from what it believes explains those observations. We therefore represent explanatory hypotheses explicitly. For a current state $z_t$, the system may maintain

Each hypothesis contains at least: a statement about the dynamics of the subject; predicted future observations or states; conditions under which the hypothesis should be rejected; supporting and contradicting evidence; uncertainty or confidence; version and provenance.

A hypothesis can therefore express

Crucially, competing hypotheses can coexist. The system is not required to collapse uncertainty prematurely into a single explanation. A later observation can support $H_1$, contradict $H_2$, or indicate that neither adequately explains the observed transition.

The internal model consequently evolves through explicit epistemic states:

Falsified hypotheses need not disappear. They remain part of the model's epistemic history — the system remembers not only what it currently believes, but what it tried to believe and why that explanation failed.

Consider an action $a_t$ executed under hypothesis $H_i$. The hypothesis predicts ${\hat{z}}_{t+\Delta }$. The system later observes $z_{t+\Delta }$. Their difference,

has a richer role than ordinary prediction error: it is evidence about the hypothesis that generated the prediction. A sufficiently large divergence may reduce confidence in the hypothesis, falsify it, change the estimated transition dynamics, activate an alternative hypothesis, reinterpret preceding states, invalidate dependent future predictions, and alter subsequent actions.

Failure becomes a mechanism of plasticity.

Passive observation is not always the fastest way to learn a system. Suppose two hypotheses $H_1$ and $H_2$ explain the same trajectory. For a candidate action $a$, they predict different outcomes:

The difference between these distributions gives the action epistemic value. An action can therefore be selected according to an objective of the form

where $U(a)$ is expected progress toward a target state, $I(a;H)$ is expected information gain over competing hypotheses, $C(a)$ is cost or burden, and $R(a)$ is risk.

The optimal action can simultaneously move the system toward a desired state and distinguish between explanations of its dynamics. Measurement itself becomes an action when its primary effect is reduction of uncertainty. The resulting loop is:

The system does not simply act according to its model. It acts partly to improve the model.

Every completed interaction creates a transition observation $(z_t,a_t,z_{t+\Delta })$. A persistent system accumulates these transitions longitudinally:

These trajectories allow the transition model itself to evolve. Starting from an initial model $f_{{\theta }_0}$, experience produces

The system progressively learns

rather than relying exclusively on a transition function learned before deployment. This is continuous system identification. It is particularly valuable when population-level dynamics provide a useful prior but individual dynamics differ substantially.

The pretrained model answers: how do systems like this generally behave? The continuously identified model can increasingly answer: how does this system behave?

Traditional deployment often looks approximately like

where the model is stable and context changes. Continuous model plasticity instead gives

The important point is that ${\text{Model}}_{t+1}$ need not imply modification of every parameter — or even modification of the weights of a foundation model. Plasticity can exist in persistent state, dependency structure, transition models, uncertainty distributions, hypotheses, policies, and learned subject-specific dynamics.

The foundation model can remain a reasoning substrate while the persistent world model evolves around it. The evolving object can instead be explicit, inspectable, versioned, selectively recomputable, and reversible.

Consider two initially identical instances

that subsequently experience different trajectories ${\tau }_A\ne {\tau }_B$. After sufficient interaction:

The difference is deeper than memory contents. The two instances may now possess different reconstructions of latent state, uncertainty distributions, supported and falsified hypotheses, transition functions, expectations about future responses, information-seeking strategies, and action policies.

They have become different models through experience. The specialization is not injected as a profile. It emerges from accumulated state–action–response trajectories.

Persistent systems need to distinguish between information that changes in seconds and information that remains informative for years. Let an observation type $x$ have a characteristic validity timescale ${\tau }_x$. Confidence that an observation still describes the current state can decay with elapsed time:

A genomic property may remain stable. A physiological signal may remain informative for minutes. A behavioral state may change within hours. A relationship or preference may evolve over months.

The model should therefore not ask merely whether a statement is true. It should ask

This avoids treating temporal change as contradiction. The system can simultaneously represent

Both can be correct.

Memory and planning no longer need to be fundamentally separate systems. The historical graph contains observed and inferred states. The future graph contains predicted states and planned actions. Both are connected by the same dependency semantics.

A hypothesis explaining the past generates predictions about the future. An observation from that future eventually becomes part of the past. The boundary moves continuously:

The model is therefore continuously converting predictions into evidence. This makes time itself part of the learning architecture.

Most training datasets contain observations. Persistent closed-loop systems can produce something richer:

Repeated over the same subject, these become trajectories

Cross-sectional data can reveal correlations between states. Longitudinal intervention–response data begins to reveal transition structure. Repeated interventions under different states provide evidence about conditional dynamics:

A continuously interacting system therefore creates its own learning substrate as a consequence of operation:

Persistent world models introduce a complementary learning regime:

Offline learning provides broad priors. Lived learning identifies local dynamics. A foundation model can provide strong prior knowledge about the class of system being observed; continuous experience provides evidence about the particular instance. Formally,

becomes a prior that is progressively conditioned by an individual trajectory:

As $t$ increases, the model can become progressively more specific without discarding its general prior. This is not merely personalization: personalization changes outputs according to known characteristics, while continuous system identification learns previously unknown characteristics of the dynamics themselves.

The resulting object differs from several familiar architectures.

• More than memory, because observations modify an explicit model of state and dynamics.
• More than a temporal knowledge graph, because nodes participate in prediction, falsification, and control.
• More than a state estimator, because the transition dynamics and explanatory hypotheses are themselves revisable.
• More than a digital twin, because the dynamics need not be known when the model is instantiated.
• More than a control policy, because actions are selected partly to discover the system being controlled.

Its core computational object is not a growing collection of experiences. It is the evolving relationship

First, experience can become cumulative without requiring unlimited context. Historical observations can be compressed into state, transitions, hypotheses, and dependency structures while preserving provenance.

Second, uncertainty becomes actionable. The system can seek the observation that would most reduce uncertainty relevant to a decision.

Third, mistakes become durable learning events. A falsified hypothesis remains represented and can prevent the same explanatory failure from being repeatedly rediscovered.

Fourth, individualization can occur at the dynamics level. The system learns not simply characteristics of a subject but how that subject changes.

Fifth, longitudinal interaction becomes increasingly valuable. A long-lived model possesses transition evidence unavailable to a newly instantiated model even when both share the same foundation model.

Finally, two systems beginning with identical priors can become meaningfully different computational objects through different lived trajectories. That may be one of the most important consequences of persistent AI.

The dominant abstraction for persistent AI has been memory.

Memory is necessary, but memory alone does not capture what becomes possible when an AI system interacts repeatedly with the same evolving system.

A persistent model can observe state, maintain competing explanations, predict transitions, choose actions that both act and learn, observe the resulting response, falsify incorrect explanations, reconstruct its interpretation of the past, and update its model of future dynamics. The resulting loop is:

Over time, the system does not simply accumulate a larger record of the world. It becomes increasingly shaped by the dynamics of the world it has experienced.

A memory system becomes larger with experience. An adaptive world model becomes different.